Question: Simplify the following expression: $k = \dfrac{9p^3}{-36p^3 - 63p^2}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $9p^3 = (3\cdot3 \cdot p \cdot p \cdot p)$ The denominator can be factored: $-36p^3 - 63p^2 = - (2\cdot2\cdot3\cdot3 \cdot p \cdot p \cdot p) - (3\cdot3\cdot7 \cdot p \cdot p)$ The greatest common factor of all the terms is $9p^2$ Factoring out $9p^2$ gives us: $k = \dfrac{(9p^2)(p)}{(9p^2)(-4p - 7)}$ Dividing both the numerator and denominator by $9p^2$ gives: $k = \dfrac{p}{-4p - 7}$